Heretofore, an aluminum or aluminum alloy substrate has been treated with an etching type strong alkaline cleaning solution and rinsed with water and treated by a chromate treatment or an Alumite treatment in a surface treatment of an aluminum or aluminum alloy substrate. However, the chromate treatment has disadvantages of an environmental pollution and a toxicity to human-body and a difficulty of disposal of a wasted sludge. On the other hand, the Alumite treatment has economical disadvantages of a requirement of a large apparatus and a large consumption of electric power.